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UPDATED: The four French Jews gunned down at a kosher supermarket in the east of Paris have been buried in Jerusalem.

Yoav Hattab, Philippe Braham, Yohan Cohen and Francois-Michel Saada were at the kosher supermarket in eastern Paris on Friday shortly before the start of the Jewish sabbath when it was attacked by Islamist gunman Amedy Coulibaly.

All four were shot dead and another 15 people taken hostage by Coulibaly before police stormed the building, killing him.

Coulibaly had links to the two Islamic extremists behind the massacre of 12 people at the Paris offices of satirical weekly Charlie Hebdo two days earlier.

Israel Prime Minister Benjamin Netanyahu agreed to a request from the families that the victims be buried in Jerusalem.

As the funeral commenced at the sprawling Givat Shaul cemetery on the city's western outskirts, thousands were on hand in an atmosphere of shock and grief, with rabbis making a symbolic cut into the clothes of immediate family members in a traditional Jewish act of mourning.

Israeli President Reuven Rivlin said that it was unacceptable that Jews fear to walk the streets of Europe seven decades after the Nazi Holocaust.

A mourner at the funeral. Photo: AFP

"We cannot allow that in 2015, 70 years since the end of World War II, Jews are afraid to walk in the streets of Europe with skullcaps and tzitzit," he said of the traditional headcovering and prayer garments worn by religious Jews.

Rivlin was joined in the ceremony by Netanyahu, opposition leader Isaac Herzog, and other Israeli ministers and officials.

Members of Israel's French-speaking community were also on hand.

The four bodies were released from the forensic institute in Paris on Monday and flown to Israel. The victims' families were also on the flight.

For many, the supermarket attack brought back memories of another deadly shooting in the southern French city of Toulouse in March 2012 when Islamist gunman Mohamed Merah shot dead three young children and a teacher at a Jewish school.

All four were flown to Israel where they were buried in the same Jerusalem cemetery where the victims from the latest shooting will also be laid to rest.